Electrically controlled systems often respond, at least in part, to external events. Sensors of various kinds are typically utilized to allow such a system to monitor the desired external events. Such sensors provide predictable electrical responses to specific environmental stimuli. Sensors are comprised of one or more components, and such components are usually only accurate within some degree of tolerance. As a result, sensors are calibrated prior to installation and use.
However, such calibration techniques are relatively costly. Instead, a data base can be empirically prepared for each sensor to relate that sensor's output to known environmental influences. Such an apparatus and method for calibrating a sensor was recently patented (PCT/US86/00908; see WO 87/00267 of Jan. 15, 1987). However, such a complete empirical data base may still be much too expensive to prepare and update in real-time for every sensor of a large sensor system.
Fortunately, it has turned out that there seldom is an absolute need for such an empirical data base if the sensor system only has some data-redundancy or overdetermination in it (see Antti A. Lange, 1986: "A High-pass Filter for Optimum Calibration of Observing Systems with Applications"; pages 311-327 of "Simulation and Optimization of Large Systems", edited by Andrzej J. Osiadacz and published by Clarendon Press/Oxford University Press, Oxford, UK, 1988a).
It has for a much longer time been known how the calibration of relatively small sensor systems can be maintained in real-time by using various computational methods under the general title of Kalman Filtering (Kalman, 1960; and Kalman and Bucy, 1961). However, certain stability conditions must be satisfied otherwise all the estimated calibration and other desired parameters may start to diverge towards false solutions when continuously updated again and again.
Fortunately, certain observability and controllability conditions guarantee the stability of an optimal Kalman Filter. These conditions together with a strict optimality usually require that a full measurement cycle or even several cycles of an entire multiple sensor system should be able to be processed and analysed at one time. However, this has not been possible in large real-time applications. Instead, much faster suboptimal Kalman Filters using only a few measurements at a time are exploited in the real-time applications of navigation technology and process control.
Unfortunately, the prior art real-time calibration techniques either yield the severe computation loads of optimal Kalman Filtering or their stability is more or less uncertain as it is the situation with suboptimal Kalman Filtering and Lange's High-pass Filter. A fast Kalman Estimation algorithm has been reported but it only applies to a restricted problem area (Falconer and Ljung, 1978: "Application of Fast Kalman Estimation to Adaptive Equalization", IEEE Transactions on Communications, Vol. COM-26, No. 10, October 1978, pages 1439-1446).
There exists a need for a calibration apparatus and method for large sensor systems that offers broad application and equal or better computational speed, reliability, accuracy, and cost benefits.